Detecting shifts in nonlinear dynamics using Empirical Dynamic Modeling with Nested-Library Analysis

Abrupt changes in system states and dynamical behaviors are often observed in natural systems; such phenomena, named regime shifts, are explained as transitions between alternative steady states (more generally, attractors). Various methods have been proposed to detect regime shifts from time series data, but a generic detection method with theoretical linkage to underlying dynamics is lacking. Here, we provide a novel method named Nested-Library Analysis (NLA) to retrospectively detect regime shifts using empirical dynamic modeling (EDM) rooted in theory of attractor reconstruction. Specifically, NLA determines the time of regime shift as the cutting point at which sequential reduction of the library set (i.e., the time series data used to reconstruct the attractor for forecasting) optimizes the forecast skill of EDM. We illustrate this method on a chaotic model of which changing parameters present a critical transition. Our analysis shows that NLA detects the change point in the model system and outperforms existing approaches based on statistical characteristics. In addition, NLA empirically detected a real-world regime shift event revealing an abrupt change of Pacific Decadal Oscillation index around the mid-1970s. Importantly, our method can be easily generalized to various systems because NLA is equation-free and requires only a single time series.Author summary: Abrupt shifts in system dynamics, referred to as regime shifts, are common in natural systems and pose significant challenges for system management and risk assessment. Accurately detecting the change point that separates pre- and post-regime shift periods is crucial, as the data collected after regime shift can be more informative to forecast future system states. While numerous methods have been proposed to tackle this issue, identifying change points in chaotic systems remains difficult, in which regime shift signals can be concealed by chaotic dynamics. To address this issue, we propose Nested-Library Analysis (NLA), a machine learning method rooted in a data-driven, nonparametric framework for nonlinear dynamical systems, known as Empirical Dynamic Modeling (EDM). NLA effectively identifies the change points from time series data, even when the shifts in dynamics are nearly imperceptible due to chaotic behavior, surpassing the existing change point detection methods. As such, our method offers a generic solution for revealing the timing of regime shifts in a various type of dynamical system.